We will be arriving in Florence in September and would like to also spend time at a coastal area. We do not want to hire a car but still want to see surrounding areas. What would you suggest as places to stay as bases and how long in each place.
Normally I would suggest getting a car because you can see so much more but ... if you really don't want to rent a car then you can travel the coast starting from Livorno by train - these train stops are not always ON the beach - but if you arrange for a taxi with your hotel - or a local shuttle bus you can go from your accommodations to the beaches.
Some of the towns that I have been too along the coast which I find to be pretty characteristic of the area include:
Cecina, one of the larger cities along the coast
Bolgheri is a bit of a mix between hillside town and a beach town